Why does the air temperature at different altitudes change?

Well, why does the temperature in different areas change? The same locations can't be the same temperature. Just as the closer to the North and South pole means the temperature will be colder, the higher you are from the ground, the colder it will be, generally speaking.

The sun doesn't really do much to warm the air, it warms the ground, and the ground warms the air. That's why the temperature doesn't do a near-instant drop when the sun goes down. Since the ground is the heat source, the higher up, the further from the heat source, and thus the colder it is.

With that being said, temperatures can be warmer higher up, due to the fact that the air is constantly moving. Jet streams are very good at transferring warm and cold air, at levels far above the ground. Warmer air will warm the surrounding air, slightly cooling off as the heat exchanges, further contributing to different temperatures at ground level, as well as above it. Of course, the reverse effect happens with cold air; it will cool off the air around it, assuming it is colder than the air, warming up when the heat exchanges. Air temperature changes because of differing air pressures.